Single photon counting plays an essential role for a wide variety of applications, ranging from biomedical research to astronomy. In gamma-ray astronomy, the Cherenkov telescope MAGIC is used to detect Cherenkov photons generated in atmospheric air showers. Since the flux of Cherenkov photons from air showers is low, the development of new single photon detectors with high quantum efficiency is necessary. The concept of the Back Illuminated Drift Silicon Photomultiplier (BID SiPM) is a novel detector design for single photon counting. It combines the principles of a silicon photomultiplier (SiPM) and a drift diode. The back illuminated drift silicon photomultiplier is operated as back illuminated detector thus providing a fill factor of 100%. A high quantum efficiency of about 80% in a wavelength region of 300 - 1000 nm can be achieved. The drift region is used to focus electrons from the back through the depleted bulk to the small point-like avalanche region. The time jitter of the electrons limits the time resolution of the detector to about 1 ns as simulation results show. A prototype of an avalanche region which can be combined with a drift structure was produced at the MPI Semiconductor Laboratory as proof of principle. The detector concept and results of measurements of dark rate and leakage current are presented.